Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medical image analysis with both population trends and random subject specific variation. Focusing on a stochastic extension of the LDDMM models with evolutions governed by a stochastic EPDiff equation, we use moment approximations of the corresponding Ito diffusion to construct estimators for statistical inference in the full stochastic model. We show that this approach, when efficiently implemented with automatic differentiation tools, can successfully estimate parameters encoding the spatial correlation of the noise fields on the image

翻译：视觉图像变形模型模型可以研究通过变形图像域来改变图像而使图像变形的时间-持续随机的随机图像变形效应。应用包括包含人口趋势以及随机特定主题变异的纵向医学图像分析。侧重于LDDMM模型的随机扩展,其演化由随机 EPDiff 等式调节,我们使用相应的Ito扩散瞬时近似值来构建完整随机模型中统计推导的估测器。我们表明,这种方法如果在自动区分工具的有效实施下,能够成功地估计将图像上噪音场的空间相关性编码的参数。